Unifying inference for semiparametric regression

2021 ◽  
Author(s):  
Shaoxin Hong ◽  
Jiancheng Jiang ◽  
Xuejun Jiang ◽  
Zhijie Xiao
Keyword(s):  
Stock Returns ◽  
Empirical Likelihood ◽  
Semiparametric Regression ◽  
Confidence Regions ◽  
Least Square ◽  
State Variables ◽  
Finite Sample ◽  
Inference Procedure ◽  
Partially Linear ◽  
Predictive Regressions

Abstract In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favorable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

scholarly journals Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

2022 ◽  
Vol 9 ◽  
Author(s):  
Xiuzhen Zhang ◽  
Riquan Zhang ◽  
Zhiping Lu
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Long Memory ◽  
Score Function ◽  
Real Data ◽  
Confidence Regions ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Finite Sample ◽  
Memory Time

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

scholarly journals Upper Bounds on Return Predictability

2017 ◽  
Vol 52 (2) ◽  
pp. 401-425 ◽  
Author(s):  
Dashan Huang ◽  
Guofu Zhou
Keyword(s):  
Stock Returns ◽  
Upper Bounds ◽  
Future Research ◽  
State Variables ◽  
Discount Factors ◽  
Predictive Regressions ◽  
Market Portfolio ◽  
Stochastic Discount Factors ◽  
Highly Correlated ◽  
Using Data

Can the degree of predictability found in data be explained by existing asset pricing models? We provide two theoretical upper bounds on theR2of predictive regressions. Using data on the market portfolio and component portfolios, we find that the empiricalR2s are significantly greater than the theoretical upper bounds. Our results suggest that the most promising direction for future research should aim to identify new state variables that are highly correlated with stock returns instead of seeking more elaborate stochastic discount factors.

scholarly journals Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Yuye Zou ◽  
Chengxin Wu
Keyword(s):  
Empirical Likelihood ◽  
Error Variance ◽  
Variance Function ◽  
Likelihood Method ◽  
Coefficient Function ◽  
Errors In Variables ◽  
Finite Sample ◽  
Right Censored Data ◽  
Varying Coefficient ◽  
Partially Linear

In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. Based on regression calibration, imputation, and inverse probability weighted methods, we define a class of modified profile least square estimators of the parameter and local linear estimators of the coefficient function, which are applied to constructing estimators of the error variance function. In order to improve the estimation accuracy and take into account the heteroscedastic error, reweighted estimators of the parameter and coefficient function are developed. At the same time, we apply the empirical likelihood method to construct confidence regions and maximum empirical likelihood estimators of the parameter. Under appropriate assumptions, the asymptotic normality of the proposed estimators is studied. The strong uniform convergence rate for the estimators of the error variance function is considered. Also, the asymptotic chi-squared distribution of the empirical log-likelihood ratio statistics is proved. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. Meanwhile, one real data example is provided to illustrate our methods.

Empirical Likelihood Inference for a Partially Linear Model under Longitudinal Data

2013 ◽  
Vol 353-356 ◽  
pp. 3355-3358
Author(s):  
Yu Ying Jiang
Keyword(s):  
Longitudinal Data ◽  
Linear Model ◽  
Empirical Likelihood ◽  
Confidence Regions ◽  
Repeated Measurements ◽  
Correlation Structure ◽  
Regression Coefficients ◽  
Partially Linear Model ◽  
Chi Square ◽  
Partially Linear

In this paper, a partially linear model under longitudinal data is considered. In order to take into consideration the within-subject correlation structure of the repeated measurements, an empirical likelihood incorporating the correlation structure is developed. The asymptotic normality of the maximum empirical likelihood estimates of the regression coefficients is obtained. It also can be shown that the proposed empirical likelihood ratio is asymptotically standard chi-square. The results can be used directly to construct the asymptotic confidence regions of the regression coefficients. The convergence rate of the baseline function is derived.

scholarly journals Empirical Likelihood for Partially Linear Single-Index Models under Negatively Associated Errors

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xin Qi ◽  
ZhuoXi Yu
Keyword(s):  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Confidence Regions ◽  
Likelihood Method ◽  
Negatively Associated ◽  
Single Index ◽  
Index Model ◽  
Partially Linear ◽  
Blockwise Empirical Likelihood ◽  
Parameters Of Interest

In this paper, the authors consider the application of the blockwise empirical likelihood method to the partially linear single-index model when the errors are negatively associated, which often exist in sequentially collected economic data. Thereafter, the blockwise empirical likelihood ratio statistic for the parameters of interest is proved to be asymptotically chi-squared. Hence, it can be directly used to construct confidence regions for the parameters of interest. A few simulation experiments are used to illustrate our proposed method.

scholarly journals Moment Conditions Selection Based on Adaptive Penalized Empirical Likelihood

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Yunquan Song
Keyword(s):  
Empirical Likelihood ◽  
Real Life ◽  
Confidence Regions ◽  
Tuning Parameter ◽  
Finite Sample ◽  
Unknown Parameters ◽  
Moment Conditions ◽  
Moment Selection ◽  
Finite Sample Properties ◽  
Shrinkage Method

Empirical likelihood is a very popular method and has been widely used in the fields of artificial intelligence (AI) and data mining as tablets and mobile application and social media dominate the technology landscape. This paper proposes an empirical likelihood shrinkage method to efficiently estimate unknown parameters and select correct moment conditions simultaneously, when the model is defined by moment restrictions in which some are possibly misspecified. We show that our method enjoys oracle-like properties; that is, it consistently selects the correct moment conditions and at the same time its estimator is as efficient as the empirical likelihood estimator obtained by all correct moment conditions. Moreover, unlike the GMM, our proposed method allows us to carry out confidence regions for the parameters included in the model without estimating the covariances of the estimators. For empirical implementation, we provide some data-driven procedures for selecting the tuning parameter of the penalty function. The simulation results show that the method works remarkably well in terms of correct moment selection and the finite sample properties of the estimators. Also, a real-life example is carried out to illustrate the new methodology.

scholarly journals TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS

2010 ◽  
Vol 26 (6) ◽  
pp. 1761-1806 ◽  
Author(s):  
Liangjun Su ◽  
Halbert White
Keyword(s):  
Structural Change ◽  
Linear Models ◽  
Linear Time ◽  
Semiparametric Regression ◽  
Parametric Models ◽  
Finite Sample ◽  
Weighted Residuals ◽  
Partially Linear ◽  
Finite Sample Properties ◽  
Cumulative Sums

We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests under the null hypothesis of no structural change and for sequences of local alternatives. We show that the tests are generally not asymptotically pivotal under the null but may be free of nuisance parameters asymptotically under further asymptotic stationarity conditions. Our tests thus complement the conventional instability tests for parametric models. To improve the finite-sample performance of our tests, we also propose a wild bootstrap version of our tests and justify its validity. Finally, we conduct a small set of Monte Carlo simulations to investigate the finite-sample properties of the tests.

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